OFFSET
0,8
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
Euler transform of period 18 sequence [1, -1, 1, -1, 1, -3, 1, -1, 4, -1, 1, -3, 1, -1, 1, -1, 1, 0, ...].
a(3*n) = A132179(n). a(3*n + 2) = 0.
Expansion of psi(x) * f(-x^6)^2 / f(-x^9)^3 in powers of x where psi(), f() are Ramanujan theta functions. - Michael Somos, Aug 10 2017
EXAMPLE
G.f. = 1 + x + x^3 - x^6 - 2*x^7 + x^9 + 4*x^10 - x^13 - 3*x^15 - 8*x^16 + ...
G.f. = 1/q + q + q^5 - q^11 - 2*q^13 + q^17 + 4*q^19 - q^25 - 3*q^29 - 8*q^31 + ...
MATHEMATICA
eta[x_] := x^(1/24)*QPochhammer[x]; A182036[n_] := SeriesCoefficient[q^(1/2)*(eta[q^2]* eta[q^6])^2/(eta[q]*eta[q^9]^3), {q, 0, n}]; Table[A182036[n], {n, 0, 50}] (* G. C. Greubel, Aug 09 2017 *)
a[ n_] := SeriesCoefficient[ 1/2 x^(-1/8) EllipticTheta[ 2, 0, x^(1/2)] QPochhammer[ x^6]^2 / QPochhammer[ x^9]^3, {x, 0, n}]; (* Michael Somos, Aug 10 2017 *)
PROG
(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^6 + A)^2 / (eta(x + A) * eta(x^9 + A)^3), n))};
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Apr 07 2012
STATUS
approved